To add on, you can help yourself here by taking advantage of every situation that gives you a longer than normal window to react to procs.

Tacking an ogcd attack on after Split Shot for example will give you a more generous window to react to a Slug Shot proc.

If something important like Hot Shot/Lead Shot is falling off soon (~3 seconds, for example). You have time to cast Split Shot once, and then because refreshing Hot Shot/Lead Shot has priority at this point, you can leisurely check if your Split Shot procced a Slug Shot while refreshing Hot Shot/Lead Shot.

In cases where your reaction to procs is not 100% perfect, it's little things like this that will give you marginal DPS increases, by reducing your opportunities to make a mistake.